The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Stratified least fixpoint logic
Theoretical Computer Science
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Tableau calculi for answer set programming
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
A Deductive System for FO(ID) Based on Least Fixpoint Logic
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
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The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. This paper studies a deductive inference method for PC(ID), its propositional fragment.We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our deductive system integrates inference rules for propositional calculus and definitions.We prove the soundness and completeness of this deductive system for a slightly restricted fragment of PC(ID). We also give a counter-example to show that cut-elimination does not hold in this proof system.